The random walks used to measure the ability for nodes to influence and affect the boundary nodes have a fixed number of steps.
For the walks to represent the localized region of these nodes, \(\mathbf {B}\) , the walks cannot be given an excessively large
length as this would dilute the importance of nodes closer to the boundary nodes.
The Barabási–Albert model [1]}, [2]}
uses the mechanism of preferential attachment to
reproduce the growth characteristics of many networks. The average path length for these networks is \({\text{log}(N)}{\text{log}(\text{log}(N))}\) , where we assume that
the ceiling of the value is taken.
We use this value as a baseline is deciding
the number of random walk steps that must be taken before a piece of information loses the consistency and relevance of the original content.
